Limit Cycles Bifurcating from the Quasi-Homogeneous Polynomial Centers of Weight-Degree 2 Under Non-Smooth Perturbations

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发表日期：

2025年7月2日

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Shiyou Sui,
Yongkang Zhang,
Baoyi Li

摘要

We investigate the maximum number of limit cycles bifurcating from the period annulus of a family of cubic polynomial differential centers when it is perturbed inside the class of all cubic piecewise smooth polynomials. The family considered is the unique family of weight-homogeneous polynomial differential systems of weight-degree 2 with a center. When the switching line is $x=0$ $x = 0$ or $y=0$ $y = 0$ , we obtain the sharp bounds of the number of limit cycles for the perturbed systems by using the first order averaging method. Our results indicate that non-smooth systems can have more limit cycles than smooth ones, and the switching lines play an important role in the dynamics of non-smooth systems.